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A210448
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Total number of different letters summed over all ternary words of length n.
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4
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0, 3, 15, 57, 195, 633, 1995, 6177, 18915, 57513, 174075, 525297, 1582035, 4758393, 14299755, 42948417, 128943555, 387027273, 1161475035, 3485211537, 10457207475, 31374768153, 94130595915, 282404370657, 847238277795, 2541765165033, 7625396158395, 22876389801777, 68629572058515
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OFFSET
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0,2
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COMMENTS
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These are the numbers d(n,3) studied by J. L. Martin. - N. J. A. Sloane, Sep 13 2014
For n >= 0, the number of ternary sequences of length n+1, that contain at least one pair of same consecutive digits. - Armend Shabani, Apr 10 2019
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LINKS
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FORMULA
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E.g.f.: 3*exp(3x) - 3*exp(2x).
See Mathematica code for a more transparent version of the e.g.f.
Generally for an m-ary word of length n: m*exp(m*x) - m*exp((m-1)*x)
G.f.: 3*x/((3*x-1)*(2*x-1)).
(End)
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EXAMPLE
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a(2) = 15 because the length 2 words on alphabet {0,1,2} are: 00, 01, 02, 10, 11, 12, 20, 21, 22 and we sum respectively 1 + 2 + 2 + 2 + 1 + 2 + 2 + 2 + 1 = 15.
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MAPLE
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a:= n-> 3*(3^n-2^n):
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MATHEMATICA
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nn=28; Range[0, nn]!CoefficientList[Series[D[(1+y(Exp[x]-1))^3, y]/.y->1, {x, 0, nn}], x]
(* Second program: *)
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CROSSREFS
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A diagonal of the triangle in A079268.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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